Question: Rewrite as a simplified fraction. ${0.9\overline{65} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 965.6565...\\ 10x &= 9.6565...\end{align*}}$ Subtracting the two equations, we have: ${990x = 956}$ ${x = \dfrac{956}{990}} $ ${x = \dfrac{478}{495}} $